# Labour/Labor Yield/Sub-Efficiency/Sub-Usage Variance

 A Problem
200 hrs of Skilled Labour/Labor @ Rs. 20 per hr, 400 hrs of Semi-Skilled Labour/Labor @ Rs. 15/hr and 150 hrs of Unskilled Labour/Labor @ Rs. 10 per hr were planned to be utlised for manufacturing 7,500 units of a product. 240 hrs of skilled labour/labor @ Rs. 22 per hr, 500 hrs of Semi-skilled labour/labor @ Rs. 14/hr and 220 hrs of Unskilled labour/labor @ Rs. 12 per hr were actually used for manufacturing 7,125 units of the product. 16 hrs of Skilled Labour/Labor time, 50 hrs of Semi-Skilled Labour/Labor time and 22 hrs of Unskilled Labour/Labor time were lost due to break down which is abnormal.

What is the variation in total cost on account of variation in the output/yield?
This information is provided by the labour/labor yield variance.

The problem data arranged in a working table:

Time(hrs) Rate(Rs/hr) Cost(Rs) Rate(Rs/hr) Gross/Total Net Abnromal Time(hrs) Cost(Rs) Time(hrs) Cost(Rs) Standard [Production: 7,500 units] Actual [Production: 7,125 units] Skilled 200 20 4,000 22 240 5,280 216 4,752 24 528 Semi Skilled 400 15 6,000 14 500 7,000 450 6,300 50 700 Un Skilled 150 10 1,500 12 220 2,640 198 2,376 22 264 750 11,500 960 14,920 864 13,428 96 1,492

SR(SO) =
 SCMix SO
⇒ SR(SO) =
 Rs. 11,500 7,500 units
⇒ SR(SO) =
Rs.
 23 15
/unit

 The Formulae » Labor/Labour Yield/Sub-Usage/Sub-Efficiency Variance (LYV/LSUV/LSEV)
That part of the variance in the total cost of labour/labor on account of a variation between the output that should be achieved for the net labour/labor time actually employed in production and the actual production achieved. It is a part of the Labour/Labor Usage/Efficiency Variance or a Sub-Part of the Labour/Labor Cost Variance.

It is the difference between the Standard Cost of Actual Output/Yield and the Standard Cost of Standard Output/Yield for the Actual Input (Actual Time of Mix)
⇒ Labour/Labor Yield/Sub-Usage/Sub-Efficiency Variance
= Standard Cost of Actual OutputStandard Cost of Standard Output/Yield for Actual Input

• #### For each Labour/Labor type Separately

 This variance cannot be identified for each labour/labor type separately.
• #### For all Labour/Labor types together [Total Labour/Labor Yield/Sub-Efficiency/Sub-Usage Variance :: TLYV/TLSEV/TLSUV]

TLYV = SC of AO − SC of SO for AT(N)Mix
=
(AO × SR(SO)) −
 AT(N)Mix STMix
× SO × SR(SO)
=
(AO −
 AT(N)Mix STMix
× SO) × SR(SO)

 LYV/LSEV/LSUV » Formula interpretation
The above formulae for Labour/Labor Yield/Sub-Efficiency/Sub-Usage Variance, can be used in all cases i.e. both when ATMix = STMix as well as when ATMix ≠ STMix. When ATMix ≠ STMix, the ratio ATMix/STMix works as a correction factor to readjust the ST to ST for AI and thereby the SC to SC for AI.

• #### Actual Time ⇒ Net Time

Wherever you find the presence of actual time in the formula, you should interpret it as Actual (Net) Time. Where there abnormal loss of time, the actual time is segregated into two as abnormal loss time and net time. Even in such cases, for the purpose of calculating the yield/sub-efficiency/su-usage Variance, the (Net) time should be considered for actual time.

#### Why Only Normal Time

Since, Labour/Labor Yield/Sub-Efficiency/Sub-Usage Variance is a part of the Labour/Labor Efficiency Variance which is calculated based on the normal time, we have to consider only normal time in calculating this variance.
• This formula when applied for each labour/labor type separately is nothing but the formula for Labour/Labor Efficiency Varaince for each indivdual type of labour/labor.
• #### Standard − Actual or Actual − Standard??

Say the actual yield is 2,000 units and the standard yield for actual input is 1,800 units. Does this indicate efficiency or inefficiency? Surely, efficiency since, using a resource to make 1,800 units a production of 2,000 units is obtained. This then should give us a positive variance. This would be possible only if we consider the data in the order "Actual" − "Standard". Be conscious of this, as in calculating all other labour/labor variances, we write "Standard" − "Actual".
• #### Where AT(N)Mix = STMix

AT(N)Mix/STMix becomes 1 thus nullifying its effect, in which case the formula would read as:

For all the labour/labor types together  TLYV = (AO − SO) × SP(SO)

• #### TLYV = 0

The total Labour/Labor Yield Variance would be zero, where the Standard Output for Actual Input Time (Actual Mix) and the Actual Output are equal.

Where TLYV = 0, the total Labour/Labor Efficiency Variance is on account of Labour Mix/Gang-Composition.  TLEV/TLUV = TLMV/TGCV + TLYV = TLMV/TGCV + 0 = TLMV/TGCV

• #### TLYV = TLEV

The total Labour/Labor Yield/Sub-Efficiency/Sub-Usage Variance would be equal to Total Labour/Labor Efficiency Variance where the Total Labour/Labor Mix Variance is zero.  TLEV/TLUV = TLMV/TGCV + TLYV/TLSEV/TLSUV = 0 + TLYV/TLSEV/TLSUV = TLYV/TLSEV/TLSUV

 Solution [Using the data as it is]
For working out problems with the data considered as it has been given without having to do any recalculations, use the above formulae (which are capable of being used in all cases)

Consider the working table above:

Time(hrs) Rate(Rs/hr) Cost(Rs) Rate(Rs/hr) Gross/Total Net Abnromal Time(hrs) Cost(Rs) Time(hrs) Cost(Rs) Standard [Production: 7,500 units] Actual [Production: 7,125 units] Skilled 200 20 4,000 22 240 5,280 216 4,752 24 528 Semi Skilled 400 15 6,000 14 500 7,000 450 6,300 50 700 Un Skilled 150 10 1,500 12 220 2,640 198 2,376 22 264 750 11,500 960 14,920 864 13,428 96 1,492
Using, TLYV/TLSEV/TLSUV =
(AO − {
 AT(N)Mix STMix
× SO} ) × SR(SO)
Therefore, total Labour/Labor yield Variance,
TLYV/TLSEV/TLSUV =
(7,125 units − {
 864 hrs 750 hrs
× 7,500 units} ) × Rs.
 23 15
/unit
=
(7,125 units − {1.152 × 7,500 units} ) × Rs.
 23 15
/unit
=
(7,125 units − 8,640 units) × Rs.
 23 15
/unit
=
(− 1,515 units) × Rs.
 23 15
/unit
= − Rs. 2,323 [Adv]

 Solution [Using recalculated data]
Where you find that the STMix ≠ AT(N)Mix, you may alternatively recalculate the standard to make the STMix = AT(N)Mix and use the figures relating to the recalculated standard in the working table. In such a case, the formulae that you use would look simpler (without the adjustment factor AT(N)Mix/STMix).

From the data relating to the problem, it is evident that STMix ≠ AT(N)Mix. Thus we recalculate the standard data for Actual Input [Refer to the calculations].

Consider the recalculated standard data and the actual data arranged in a working table.

Time(hrs) Rate(Rs/hr) Cost(Rs) Rate(Rs/hr) Total Normal Abnromal Time(hrs) Cost(Rs) Time(hrs) Cost(Rs) Standard [Production: 8,640 units] Actual [Production: 7,125 units] Skilled 230.4 20 4,608 22 240 5,280 216 4,752 24 528 Semi Skilled 460.8 15 6,912 14 500 7,000 450 6,300 50 700 Un Skilled 172.80 10 1,728 12 220 2,640 198 2,376 22 264 864 13,248 960 14,920 864 13,428 96 1,492
 Using, TLYV?TLSEV/TLSUV = (AO − SO) × SR(SO)
Therefore, total Labour/Labor yield Variance,

TLYV/TLSEV/TLSUV =
(7,125 units − 8,640 units) × Rs.
 23 15
/unit
=
(− 1,515 units) × Rs.
 23 15
/unit
= − Rs. 2,323 [Adv or Unf]

#### Note:

This formula can be used only when AT(N)Mix = STMix

#### You don't need to recalculate the standard

The formula with the adjustment factor AT(N)Mix/STMix can be used in all cases i.e. both when AT(N)Mix = STMix and AT(N)Mix ≠ STMix. Therefore, you don't need to rebuild the working table by recalculating the standards for the purpose of finding the variances.

#### Check:

The same problem was solved in both the cases above. The only difference being that in the second case, the data was considered by recalculating the Standard for Actual Input to make AT(N)Mix = STMix.

 Formulae using Inter-relationships among Variances
These formulae can be used both for each labour/labor type separately as well as for all the labour/labor types together
1. LEV/LUVN = LMV/GCV + LYV/LSUV   ⇒ (1)
• #### For each Labour/Labor Type Separately

 LYV/LSUVLab = LEV/LUV(N)Lab − LMV/GCVLab
• #### For All Labour/Labor Types Together

 TLYV/TLSEV/TLSUV = TLEV/TLUVN − TLMV/TGCV
2. LCV = LRPV + LMV/GCV + LYV/LSUVN + LITV   ⇒ (2)
• #### For each Labour/Labor Type Separately

 LYV/LSUV(N)Lab = LCVLab − LRPVLab − LMV/GCVLab − LITVLab
• #### For All Labour/Labor Types Together

 TLYV/LSUV(N) = TMCV − TMPV − TLMV/TGCV − TLITV

## Verification

The interrelationships between variances would also be useful in verifying whether our calculations are correct or not. After calculating all the variances we can verify whether
1. TLMV and TLYV add up to TLEV. If we find it so, we can assume our calculations to be correct.
2. TLMV, TLYV, TLITV and TLRPV add up to TLCV. If we find it so, we can assume our calculations to be correct.

We used the same set of data in all the explanations. Using the figures obtained for verification.

 TLMV + TLYV = (+ Rs. 198) + (− Rs 2,323) = (− Rs. 2,125) = TLEV → TRUE
 TLRPV + TMMV + TLYV + TLITV = (− Rs. 420) + (+ Rs. 198) + (− Rs. 2,323) + (− Rs. 1,450) = (− Rs. 3,995) = TLCV → TRUE

 Who is held responsible for the Variance?
 Since this variance is on account of more or less yield for the labour/labor time used, the people or department responsible for production (say manufacturing department) can be held responsible for this variance.
 Author Credit : The Edifier ... Continued Page L:12